[Independent Random Variables] Suppose that X and Y are independent exponentially distributed random variables with parameters and respectively. Let U = min(X, Y ), and V = max(X, Y ). (a) Find the marginal pdfs of U and V . (b) Are U and V independent? (c) Let W = V U. Prove that W and U are independent. (Hint: to find the joint cdf of U and W, partition the space based on whether U = X or U = Y .)